skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Mazur, Barry"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; (, Journal of Number Theory)
    Full Text Available 
  2. ; ; (, Acta Arithmetica)
    We consider first-order definability and decidability questions over rings of integers of algebraic extensions of $$\Q$$, paying attention to the uniformity of definitions. The uniformity follows from the simplicity of our first-order definition of $$\Z$$. Namely, we prove that for a large collection of algebraic extensions $$K/\Q$$, $$ \{x \in \oo_K : \text{$$\forall \e \in \oo_K^\times \;\exists \delta \in \oo_K^\times$ such that $$\delta-1 \equiv (\e-1)x \pmod{(\e-1)^2}$$}\} = \Z $$ where $$\oo_K$$ denotes the ring of integers of $$K$$. One of the corollaries of our results is undecidability of the field of constructible numbers, a question posed by Tarski in 1948. \end{abstract} 
    more » « less
    Full Text Available 
  3. ; ; (, Notices of the International Consortium of Chinese Mathematicians)
    Full Text Available